What is the value of the positive integer k?

Question

1) When k is divided by 3, the remainder is 2.
2) When k is divided by 5, the remainder is 1

Hatakekakashi · Answer

Statement 1-

k mod 3 = 2

k is in the form of 3a + 2 where a belongs to +ve integers 
k can be 2 or 5

insufficient

Statement 2 -

K mod 5 = 1

k is in the form of 5a +1 where a belongs to +ve integers 
K can be 1 or 6

Combining 1 and 2

k mod 3 = 2 2,5,8,11
k mod 5 = 1

11 is the first number and lcm of 3,5 = 15

11,26, 41

all satisfy k mod 3 = 2 and k mod 5 = 1

Hence E

amanvermagmat · Answer

Statement 1

K is an integer of the form 3x + 2. But there are infinite such integers possible (2, 5, 8, 11, 14, 17, 20, 23, 26... ).  Not sufficient .

Statement 2

K is an integer of the form 5y + 1. But there are infinite such integers possible (1, 6, 11, 16, 21, 26,...).  Not sufficient .

Combining the two statements

K = 3x + 2 = 5y + 1. 
So k is an integer which leaves remainder '2' when divided by '3', and also leaves remainder '1' when divided by '5'. We can see from the analysis of two statements that '11' is the first such number which satisfies both these conditions.

To find general formula for such kind of numbers, one method is to find LEAST such number by trial/error method. Once we have identified the least number, there is a general formula for such number which is:
 K = (Least number identified) + (LCM of divisors)*z , where 'z' is any non negative integer.

So for our given question, once we have identified least value of K to be 11, we can write a general formula for K as:
 K  = 11 + (LCM of 3&5)*z or  11 + 15*z

But since z can take infinite values, our number K can also take infinite values. Eg., 11, 26, 41, 56, ... 
Thus combined also the statements are  not sufficient  to answer the question.

Hence  E answer

MathRevolution · Answer

=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (k) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
Two possible values of k which satisfy condition 1) are 5 and 8.
Since it does not give us a unique value of k, condition 1) is not sufficient.

Condition 2):
Two possible values of k which satisfy condition 2) are 1 and 6.
Since it does not give us a unique value of k, condition 2) is not sufficient.

Conditions 1) & 2): 
Two possible values of k which satisfy both conditions 1) & 2) are 11 and 26.
Since they do not give us a unique value of k, conditions 1) & 2) together are not sufficient.

Therefore, E is the answer.

Answer: E

AkshdeepS · Answer

Given : k > 0

St 1: k = 2, 5, 8, 11, 14, 17, 20, 23, 26  Insufficient

St 2: k = 1, 6, 11, 16, 21, 26  Insufficient

Combined : k = 11 or 26 or  Insufficient

(E)

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What is the value of the positive integer k?

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What is the value of the positive integer k?

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